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Simplifying 3x(x + 5) = 88 Reorder the terms: 3x(5 + x) = 88 (5 * 3x + x * 3x) = 88 (15x + 3x2) = 88 Solving 15x + 3x2 = 88 Solving for variable 'x'. Reorder the terms: -88 + 15x + 3x2 = 88 + -88 Combine like terms: 88 + -88 = 0 -88 + 15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -29.33333333 + 5x + x2 = 0 Move the constant term to the right: Add '29.33333333' to each side of the equation. -29.33333333 + 5x + 29.33333333 + x2 = 0 + 29.33333333 Reorder the terms: -29.33333333 + 29.33333333 + 5x + x2 = 0 + 29.33333333 Combine like terms: -29.33333333 + 29.33333333 = 0.00000000 0.00000000 + 5x + x2 = 0 + 29.33333333 5x + x2 = 0 + 29.33333333 Combine like terms: 0 + 29.33333333 = 29.33333333 5x + x2 = 29.33333333 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 29.33333333 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 29.33333333 + 6.25 Combine like terms: 29.33333333 + 6.25 = 35.58333333 6.25 + 5x + x2 = 35.58333333 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 35.58333333 Calculate the square root of the right side: 5.965176722 Break this problem into two subproblems by setting (x + 2.5) equal to 5.965176722 and -5.965176722.Subproblem 1
x + 2.5 = 5.965176722 Simplifying x + 2.5 = 5.965176722 Reorder the terms: 2.5 + x = 5.965176722 Solving 2.5 + x = 5.965176722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 5.965176722 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.965176722 + -2.5 x = 5.965176722 + -2.5 Combine like terms: 5.965176722 + -2.5 = 3.465176722 x = 3.465176722 Simplifying x = 3.465176722Subproblem 2
x + 2.5 = -5.965176722 Simplifying x + 2.5 = -5.965176722 Reorder the terms: 2.5 + x = -5.965176722 Solving 2.5 + x = -5.965176722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -5.965176722 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.965176722 + -2.5 x = -5.965176722 + -2.5 Combine like terms: -5.965176722 + -2.5 = -8.465176722 x = -8.465176722 Simplifying x = -8.465176722Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.465176722, -8.465176722}
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